Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:A3L-A
Session:
Number:A3L-A4
Multiple Floating-point Matrix Multiplication by Level 3 Operations.
Katsuhisa Ozaki, Takeshi Ogita, Siegfried M. Rump, Shin’ichi Oishi,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
This paper is concerned with accurate matrix multiplication. First we define a form which is expressed by an unevaluated summation of some floating-point numbers in order to have many bits. We call this form ‘multiple floating-point numbers’. We propose an algorithm which computes matrix multiplication on this form and outputs an accurate result by mainly using Level 3 operations in BLAS. It is easy for the proposed algorithm to implement and compute in parallel. Numerical results are also presented in order to illustrate the efficiency of the proposed method.